There are two main "slices" of a circle:
The "pizza" slice is called a Sector. *white selection below*
And the slice made by a chord is called a Segment. *white selection below*
Lets take a look at this in Softimage.... |
* Watch in highest quility possible*
To work out the area of the segment and sector you will use the formulas:
Area of Sector = ½ × (θ × π/180) × r2 (when θ is in degrees)
Area of Segment = ½ × ( (θ × π/180) - sin θ) × r2 (when θ is in degrees)
*So basically what we need is the angle of the "center" corner, and the radius of the circle the sector belongs too*
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What these formulas will look like in ICE - once you have the angle and raduis - :
Segment area:
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Sector area:
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So you will need to work out the lengths of the three sides of the triangle that fits inside the sector "pizza slice".
I did this by simple creating cluster centers on the last point of the three curves then getting the length between them....
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Here are the tree's for that...
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....then you can work out the angle of the center corner in the circle your sector is part of.
I used the standard law of cosines node for this one but here is the math formula:
cos A = (b2 + c2 - a2)/2bc
I used this law because I already had all three side lengths worked out, but never fear here is a link to other ways of working out you triangles if you have say one angle and two sides...
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You can also work out the "arc length" - the blue line in the image below - of your sector, by using the formula:
L = (θ × π/180) × r
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Here's that ICE tree...
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And there you have it. If you ever need to work out how big a pizza slice is ..... now you can do it :)
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